Cutting Cognitive Research: Principles and Implications (2016) 1:30 Cognitive Research: Principles DOI 10.1186/s41235-016-0029-0 and Implications

ORIGINALARTICLE Open Access The evolution of pace in popular movies James E. Cutting

Abstract Movies have changed dramatically over the last 100 years. Several of these changes in popular English-language filmmaking practice are reflected in patterns of film style as distributed over the length of movies. In particular, arrangements of shot durations, motion, and luminance have altered and come to reflect aspects of the narrative form. Narrative form, on the other hand, appears to have been relatively unchanged over that time and is often characterized as having four more or less equal duration parts, sometimes called acts – setup, complication, development, and climax. The altered patterns in film style found here affect a movie’s pace: increasing shot durations and decreasing motion in the setup, darkening across the complication and development followed by brightening across the climax, decreasing shot durations and increasing motion during the first part of the climax followed by increasing shot durations and decreasing motion at the end of the climax. Decreasing shot durations mean more cuts; more cuts mean potentially more saccades that drive attention; more motion also captures attention; and brighter and darker images are associated with positive and negative emotions. Coupled with narrative form, all of these may serve to increase the engagement of the movie viewer. Keywords: Attention, Emotion, Evolution, Film style, Movies, Narrative, Pace, Popular culture

Significance understanding of movie structure and of movie cognition Experiments in cognitive psychology have shown us that (for example, Hasson, Mallach, & Heeger, 2010; Zacks, rapid changes in the visual field attract our eye move- Speer, Swallow, & Maley, 2010) continues to open a new ments and attention. This has been demonstrated many window onto the study of mental processes as they work times in the laboratory (see, for example, Theeuwes, 1991) continuously over spans of up to 2 h and more. and also when people watch movie clips (Smith, 2012). Many other laboratory studies have shown that motion Background also captures attention (see, for example, Franconeri & Simons, 2003), which has also been shown for people [E]very shade of feeling and emotion which fills the watching sections of movies (Mital, Smith, Hill, & spectator’s mind can mold the scenes in [a movie] Henderson, 2011). Still other controlled studies have until they appear the embodiment of our feelings.… If shown that we have positive associations to brightness and this is the outcome of esthetic analysis on the one negative associations to darkness (Valdez & Mehrabian, side, of psychological research on the other, we need 1994), a finding also found for people watching short only combine the results of both into a unified movies (Tarvainen, Westman, & Oittinen, 2015). Rapid principle: the [movie] tells us the human story by transients (cuts), motion changes, and luminance changes overcoming the forms of the outer world, namely, have been endemic to movies for a century, and they are space, time, and causality, and by adjusting the events components of what film editors call pace. Nonetheless, it to the forms of the inner world, namely, attention, has taken most of that century for filmmakers to learn to memory, imagination, and emotion. fashion their tools of film style, creating a film form that couples these three physical changes (and their Hugo Münsterberg (1916, p. 74, italics in the original)1 psychological implications) to narrative structure. A better

Movies, psychology, and pace Correspondence: [email protected] Department of Psychology, Cornell University, Uris Hall, 109 Tower Road, Ithaca, As a psychologist, Münsterberg was overwhelmed by NY 14853-7601, USA movies, but so were the increasingly large audiences that

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viewed them in the 1910s. Moreover, throughout the the movie selected from among the panoply of possibil- intervening century, movies have never lost their grip on ities within film style. popular culture, and, with mobile technologies, they Fabula is the Russian Formalist term for the underlying have become more prevalent than ever. The British Film story. The most common other terms used in this context Institute (2012, p.141) estimated that the average citizen are narrative (Bordwell, 2008) and, of course, story (Chat- in the United Kingdom sees more than 80 films per year. man, 1980). Story and narrative are perfectly acceptable syn- Although this estimate seems overly enthusiastic, it be- onyms, so I will use them here as well. The fabula is all speaks an impressive penetration of film media into about content. Importantly, just as the art of writing a novel everyday life. Popular films have become mind candy. is in the conversion of ideas into words on a page, Shklovsky In addition, few art forms have changed as much as suggested that the art of filmmaking is in the conversion of movies over the last 100 years. Some of the literature ad- the fabula into the syuzhet (Schmid, 2010, p. 178). dressing this change has focused on technology (see, for Pace and rhythm are both words used in discussions example, Salt, 1992), and there are numerous textbooks of editing. They are difficult to distinguish, so I won’t try and monographs that have traced cultural, economic, and instead will focus mostly on pace. D. W. Griffith, and political changes from the silent era to the present the esteemed early American filmmaker, may have been (see, for example, Christiansen, 1987; Kelley, 1998; first to discuss pace in the context of movies. “For its Kolker, 2006; Thompson & Bordwell, 2010). There are ability thus to lift its patrons out of commonplace exist- also treatments of the changes in physical attributes of ence, and bear them hither and yon on Bagdad [sic] car- movies, both qualitative (Bordwell, 2006) and quantita- pets to realms of adventure and romance, the [movie] tive (Bordwell, Staiger, & Thompson, 1985; Cutting, depends upon pace” (Griffith, 1926, p. 28). Beyond this DeLong, & Brunick, 2011; Cutting, DeLong, Brunick, Iri- flowery prose and other than some concrete suggestions cinschi, & Candan, 2011). Heretofore, however, there about shot duration and some oblique references to mo- have been no treatments of the psychologically relevant tion, Griffith was a little vague about what he meant by changes in these variables as they are arrayed over the pace. Pearlman (2009, p. 47) added clarity. She suggested length of entire films. This article considers three dy- that pacing refers “to three distinct operations: the rate namic patterns that are now meshed with psychological of cutting, the rate or concentration of movement or principles of attention and emotion. Before addressing change in shots and sequences, and the rate of move- them, however, let me establish some important terms ment or events over the course of the whole film.” These from the filmmaking and film studies literatures that are tasks of editing all entail manipulations of the syuzhet. pertinent to this discussion. Bordwell and Thompson (1997, p. 197; see also Polking, 1990, p. 304) drew an analogy between pace in film and tempo in music. Tempo, of course, is about time and tim- Terms ing, but it is also more. The musical tempo marking of al- Film style is the collection of all aspects of the craft of legro means “fast, quickly, and bright”;thatofvivace making movies. Filmmakers make choices about editing means “lively and fast”; and these can be modified with con (varying the length and ordering shots), staging (position- fuoco (“with fire”)andotherswithmisterioso or agitato and ing actors in front of the camera and controlling the setting dozens more. As Rao (2011, p. 17) noted, “[T]empo has behind them), framing (how much of the actors versus the three elements: rhythm, emotion, and energy.” Applied to background can be seen in the image, called shot scale), movies, Rao’s notion would be that pace might be reflected sound (controlling conversation, background noise, sound in the temporal pattern of shot durations and in the energy effects, and diegetic versus nondiegetic [background] reflected in a measure of motion – both part of Griffith’s music), camera motion, lighting, focus, color, and more. (1926) and Pearlman’s (2009) analyses – but also reflected Syuzhet is the Russian Formalist term (Bordwell, 1985; in measures relevant to emotion, the aspect of film extolled Shklovsky, 1925/1990) for the surface form of a movie – most by Tan (1996) and by Murch (2001). the particular lighting, sounds, and other aspects of film Murch (2001) strongly endorsed the centrality of emo- style that have been chosen and used over the course of tion to editing. An Academy Award-winning editor and a particular movie. Other terms used for this notion are sound designer, Murch suggested that the foremost con- plot (Barsam & Monahan, 2013), discourse (Chatman, sideration in editing is that every shot must be true to 1980), and narration (Bordwell, 2008), but I find that the emotional force of the narrative. This allegiance each of these can lead to confusion – plot can imply syn- takes precedence over advancing the story, rhythmic opsis and ignore film style, discourse can imply just the considerations, or any concern with other attributes of spoken language, and narration can imply a narrator. film style. I focus here on one particular aspect of film None of these implications is intended here. The syuzhet style that can affect a viewer’s emotional response. It is the film-length, presentational, content-free form of has been shown that people have positive associations Cutting Cognitive Research: Principles and Implications (2016) 1:30 Page 3 of 21

to brightness and negative associations to darkness symmetrically, bringing the viewer into and out of the (Valdez & Mehrabian, 1994). More importantly, this story (see also Cohn, 2014). has also been found for people watching short movies Where did this four-part structure come from? Thompson (Tarvainen et al., 2015). Thus, the empirical foci of (1999) suggested that it has been part of feature-length this paper are those correlated with filmmakers’ no- movies for a long time. In her analyses of 100 films, tions of pace: shot duration, motion, and luminance. about half of those in the 1910s and 1920s have four acts, and from the 1930s onward in her sample, four-act movies are dominant, occurring about 90% of the time. Sections of the narrative But the existence of a four-part structure is likely much Again, narratives are stories. All stories tend to be older than movies. I would claim that it has been endemic divisible into parts, often at different levels. This is true in many cultures for a long time. For example, there is a regardless of whether they are folktales (Mandler, 1978; four-part narrative tradition called kishōtenketsu found in Propp, 1928/1968), oral histories (Labov & Waletzky, Japan (Berndt, 2013), and many of the Russian folktales 1967), plays (MacEwan, 1900), comics (Cohn, 2013), or analyzed by Propp (1928/1968) have four parts, as do movies (Field, 2005; Thompson, 1999). At one level, these other tales analyzed by Mandler (1978). parts can be called events, sometimes coarse-level events Perhaps most convincing in this domain is the work (Zacks et al., 2010; Zacks & Swallow, 2007). In movies, by Labov and Waletzky (1967), who showed that spon- these are typically story units called scenes that take place taneous life stories elicited from inner-city individuals in a given location, with particular characters, within a without formal education tend to have four parts: an constrained amount of time (Cutting, 2014a), and that orientation section (where the setting and the protagonist time is typically in the domain of a minute or longer. But are introduced), a complication section (where an inciting there is also a superordinate structure to narratives. incident launches the beginning of the action), an evalu- In many cases, and particularly in movies, story form ation section (which is generally focused on a result), and can be shown to have three or four parts, often called a resolution (where an outcome resolves the complica- acts (Bordwell, 2006; Field, 2005; Thompson, 1999). The tion). The resolution is sometimes followed by a coda, term act is borrowed from theater, but it does not imply much like the epilogue in Thompson’s analysis. In sum, a break in the action. Instead, it is a convenient unit although I wouldn’t claim that four-part narratives are whose size is between the whole film and the scene in universal to all story genres, they are certainly widespread which certain story functions occur. Because there is not and long-standing. much difference between the three- and four-act concep- Thus, I assume that a general narrative form of stories tions except that the latter has the former’smiddleact was in place in our culture at the end of the 19th cen- broken in half (which many three-act theorists acknow- tury, ready to be adopted by the first feature-length films ledge; Field, 2005), I will focus on the four-act version. of the second decade of the 20th century and then be- The first act is the setup, and this is the portion of the yond. That form entails at least three, but usually four, story where listeners, readers, or viewers are introduced acts of roughly equal length. Why equal length? The rea- to the protagonist and other main characters, to their son is unclear, but Bordwell (2008, p. 104) suggested this goals, and to the setting in which the story will take might be a carryover from the development of feature place. The second act is the complication, where the films with four reels. Early projectionists had to rewind protagonists’ original plans and goals are derailed and each reel before showing the next. Perhaps filmmakers need to be reworked, often with the help or hindrance of quickly learned that, to keep audiences engaged, they other characters. The third is the development, where had to organize plot structure so that last-seen events on the narrative typically broadens and may divide into dif- one reel were sufficiently engrossing to sustain interest ferent threads led by different characters. Finally, there until the next reel began. is the climax, where the protagonist confronts obstacles to achieve the new goal, or the old goal by a different The evolution of film style as it corroborates route. Two other small regions are optional bookend-like narrative form structures and are nested within the last and the first acts. Cutting and Candan (2013) broached several issues At the end of the climax, there is often an epilogue,where about movies in relation to the other major arts, to cul- the diegetic (movie world) order is restored and loose ends ture, and to evolution. The first is that most classic art from subplots are resolved. In addition, I have suggested forms have been with us for a very long time. The ori- that at the beginning of the setup there is often a prologue gins of music, dance, sculpture, and painting are lost in devoted to a more superficial introduction of the setting our prehistory; theater and architecture are thousands of and the protagonist but before her goals are introduced years old; and, although full-flowered literature had to (Cutting, 2016). The prologue and epilogue roughly act await the printing press, it is embedded in a poetic oral Cutting Cognitive Research: Principles and Implications (2016) 1:30 Page 4 of 21

tradition that is also many thousands of years old. The character introduction. I labeled the second component longue durée (Braudel, 2009) of the presence of these art as action (21% of the variance), and it was well represented forms suggests that they may be inseparable from what by motion (eigenvector = 0.53) and by the location of ac- it means to be human. But their multimillennial span tion shots across the movies’ lengths. I labeled the third also makes it difficult to track their evolution because component as lighting (12% of the variance), well repre- culture, languages, and economies have varied dramatic- sented only by luminance (eigenvector = 0.84). Thus, there ally over time, and appropriate recording devices didn’t is some convergence between a three-dimensional notion exist to register their possible development along the way. of pace and the three dimensions that are most orthogonal Second, and in stark contrast, popular movies have in the analysis of film style as it saturates whole movies. been with us for only about 125 years. The recent devel- The focus of this article is to address the historical changes opment of this art form and the intense public interest it in pace through film style measures of shot duration, has sustained offer an intriguing possibility for studying motion, and emotion. human cognition. Although we clearly did not evolve to watch movies, it is highly likely that movies have evolved General methods in part to fit better within our cognitive and affective One hundred years of popular feature-length movies preferences and capacities. My students and I selected 210 English-language feature- Because a reasonable number of the older movies are length movies released over 100 years: 10 per year at still with us and can be analyzed by contemporary tech- 5-year intervals from 1915 to 2015. Feature length films niques, one might be able to trace the evolution of phys- are defined by the Academy of Motion Picture Arts and ical structure of the art form as it has been guided by Sciences as those at least 40 minutes in length, a duration the collectivity of filmmakers’ minds, eyes, and hands.2 necessary to be eligible for a regular Academy Award. Elsewhere, Cutting, DeLong, Brunick, Iricinschi, and These movies were among the most popular of their release Candan (2011) as well as Cutting (2014b) looked at years (http://www.boxofficemojo.com) or most rated on the changes in movies across release years and found strik- Internet Movie Database (IMDb; http://www.imdb.com). ing changes – shorter shot durations, more motion, Cutting, DeLong, and Nothelfer (2010) studied 150 of these and darker imagery over the last 60 years. But these films from 1935 to 2005 for other purposes, and Cutting, whole-film measures are coarse and fail to take into ac- DeLong, Brunick, Iricinschi, and Candan (2011) added 10 count narrative structure. My intention in this article is more from 2010 with still other goals. to track those changes as they apply to the structure of I next reduced these 160 feature-length movies to the movies as the narrative unfolds. To be sure, no psycho- 150 that were shorter than 2.5 h in duration (Cutting, logical data are gathered here; only psychologically rele- 2016). This length criterion made them better candidates vant physical measures on huge and lengthy stimuli for having a theoretical structure proposed by Thompson that have heretofore been largely ignored are covered. (1999): four roughly equal-length sequential acts – setup, In particular, I am interested in changes in syuzhets complication, development, and climax. Longer movies and how they have been shaped jointly by fabulas and may have five or even six acts, often with more than one by our cognitive and affective systems. development section. For this article, the 10 longer movies Previously, I demonstrated that a four-part narrative were replaced with 10 others of appropriate lengths and structure of the fabula has implications for syuzhet generally equal popularity from their same release year, (Cutting, 2016). I explored the variations in a dozen as- bringing the sample temporarily back up to 160. pects of film style as they are distributed along the length For this article, in addition to the 10 replacement films, of movies. These included shot duration; shot transition I added 50 more movies – 10 from 2015 and 10 each from types (cuts, dissolves, fades, and the like); shot scale; 1915, 1920, 1925, and 1930 – yielding a total of 210 motion; music; luminance; character introduction; con- movies. Like the others, the newly selected movies were versations; action shots; and across-shot changes in lo- among the most popular of their release year on IMDb. cation, characters, and time. Matching the values of Those from before 1930 are silent movies. I added the si- these variables across duration-normalized time bins in lent films to complete the investigation of feature-length 150 movies, I then performed a principal component movies in hopes of finding patterns in them that might be analysis and found that 76% of the variance could be precursors to those of later films. I couldn’t select movies accounted for by three orthogonal components. from before 1915, because the concept of feature-length Interestingly, each component aligned fairly well with film was undeveloped until the early 1910s (Pierce, 2013). one of the stimulus dimensions. For purposes of discus- Before then, almost all movies were considerably shorter sion, I labeled the first component as editing (43% of than 1 h.3 the variance). It was well captured by shot duration This century’s worth of movies contains movies of (eigenvector = 0.41), but also related to shot scale and many genres. Most are dramas, comedies, action films, Cutting Cognitive Research: Principles and Implications (2016) 1:30 Page 5 of 21

or adventure films, with some animations, crime films, each of the 100 equal-duration bins was then deter- fantasies, musicals, mysteries, science fiction movies, mined across the length of that movie. In this manner, war movies, and westerns as indicated by their first each bin had between 0 transitions (found in at least 1 genre mention on the IMDb. Although Cutting, DeLong bin in 89 different movies where it was aligned with a and Brunick (2011) and Cutting (2016) provided some long take, the term for a long-duration shot) and as analyses of genre differences, none are pursued here. All many as 80 found in 1 bin in the analysis of Avengers: 210 films are listed in the filmography below. More Age of Ultron (2015), a nearly 2.5-h movie with over importantly, I look at the changes in the temporal dynamics 3200 shots. The proportion of these transitions within across release years with an eye toward revealing the each bin was normalized by the number of shots in each evolution of movie pace and how film style has become movie (number per bin/total number of transitions), and enmeshed with narrative progression. Previously, among then values in like bins were averaged across movies. others, I analyzed these variables (Cutting, 2016) but was These means were then rescaled back to the overall unconcerned with historical changes in pace. mean shot duration across all movies (7.46 seconds) as shown in Fig. 1. The average shot duration for the silent One hundred duration-normalized time bins films was 7.5 seconds, that for the early sound films Because movies differ in their total duration, and in this 10.5 seconds, that for the midsample films 7.0 seconds, sample they varied from 50 minutes (Madame Butterfly, and that for the more contemporary movies 4.3 seconds. 1915) to 147 minutes (The Color Purple, 1985; and Motion. For a psychologist or vision scientist, motion Straight Outta Compton, 2015), each movie length was comes in several varieties (see, for example, Borst & Euler, normalized.4 That is, each movie was assigned a unit 2011), but these can be highly correlated in the real world length, the three variables measured, and the results of and in cinema (Nitzany & Victor, 2014). Thus, I have those analyses divided into 100 equal-duration time bins. investigated the easiest to measure – flicker motion (or After this, the values within like bins could be averaged flicker noise), the change in pixel values without regard to across movies and a general pattern discerned. the patterns of form that change over time and space. To Individual movies can show strikingly different pat- reduce computation time, I first downscaled each frame of terns on any given measure. Thus, this type of data is all movies to a 256 × 256 array of pixels. Then each frame quite noisy and requires pooling results over many films. (if not already in black and white) was converted to 8-bit For later analyses in this article, the 210 movies were di- grayscale (pixel values of 0–255) by the standard MATLAB vided into 4 groups – the 30 silent films (from 1915, algorithm (MathWorks, Natick, MA, USA). I then adjusted 1920, and 1925), the 60 early sound films (from 1930, the gamma of each pixel value to accord with human visual 1935, 1940, 1945, 1950, and 1955), the 60 midsample sensitivity, keeping them within the 0–255 range. films (from 1960, 1965, 1970, 1975, 1980, and 1985), and Next, I correlated the pixels in next-adjacent frames (n the 60 more contemporary films (from 1990, 1995, 2000, and n + 2) within each shot, and then I averaged the cor- 2005, 2010, and 2015). relation values within a shot.5 No comparisons were Cuts and Shot Durations. Smith and Henderson (2008) made between frames across cuts. Shot averages were showed that when individuals watch a movie with the task then assigned to the bin in which the shot began and, if of detecting cuts, they can miss as many as 20% of them; that shot stretched across the next bin, to that second and Over, Ianeva, Kraaij, and Smeaton (2007) reported bin as well. The data on which analyses were performed that the best machine algorithms at that time could do were normalized within each movie (mean = 0.0, stand- only modestly better, missing about 5% of all cuts. These ard deviation = 1.0) to nullify differences across movies values are much higher than my students and I would and emphasize only the patterns within them. Finally, as accept. Thus, we tackled the task of finding all transitions before, like-bin values were then averaged across movies. (cuts, wipes, dissolves, and fades) by manually going Luminance. Bin luminance was determined similarly, through the digital versions of each movie frame by frame. starting with the 256 × 256-pixel, gamma-transformed The 210 movies average 108 minutes in duration, or about grayscale values. All pixels were averaged within a frame 155,000 frames at 24 frames/second. and then averaged within a shot. Again, shot means were Shot durations were determined in several steps. First, assigned to the appropriate bin, normalized within each we found the number of the first frame of each new shot movie, and averages taken across like bins. in each movie, cross-checking to assure ourselves that we found (almost) all transitions, and recorded results Analytic style: polynomial regression and cross-validation on a spreadsheet. The transitional frame number for dis- As I have done previously (Cutting, 2016), I fit polynomial solves and other noninstantaneous transitions (fades and functions to the 100 bins of mean data. The sequence of wipes) was taken as its judged midpoint, thus beginning these bins will be broken into 4 equal-length regions a new shot. The number of transitions that fell within (acts), following the suggestion by Thompson (1999) that Cutting Cognitive Research: Principles and Implications (2016) 1:30 Page 6 of 21

Fig. 1 The movie-length patterns of shot duration (in seconds, left panel), of the extent of motion (middle panel), and of relative luminance (right panel) across 180 popular English-language movies released from 1930 to 2015. The lengths of the movies were normalized so that each measure was assessed across 100 equal-duration bins, and those values were normalized within each movie before averaging across them. Shot duration (converted back to seconds), flicker motion (converted back to mean correlations of eight-bit pixel values across frames), and luminance (converted back to the mean pixel value per frame) are three roughly orthogonal measures of film style (Cutting, 2016). Polynomial fits are shown as darker lines surrounded by white areas that correspond to the 95% confidence interval of that polynomial. Lighter colored regions denote the 95% confidence intervals on the data, given that polynomial. The data of each panel are also separated by vertical lines that suggest four narrative divisions (see Thompson, 1999): the setup (roughly bins 1–25), the complication (bins 26–50), the development (bins 51–75), and the climax (bins 76–100). Also noted are a prologue (initial and variable number of bins of the setup) and an epilogue (a variable number of bins at the end of the climax), optional units that do not appear in every film. A take is another name for a shot. The term long shot is reserved for a wide-angle shot, not a long-duration shot movie narratives generally consist of 4 roughly equal- produce better fits by a strict criterion. Here I will prefer length sections – the setup (here assumed to correspond a higher-order polynomial with n parameters only if it to bins 1–25), the complication (bins 26–50), the develop- produces a superior fit (measured in adjusted R2 with ment (bins 51–75), and the climax (bins 76–100). Polyno- α < .0001) to one with n − 1 parameters. I will take such mials, with their inherently curved nature, make sense in a result as a first confirmation of a reliable result. Unfortu- this context because there is variation in the length of the nately, even the use of an extremely strict criterion doesn’t acts in a given movie. Thompson’s (1999) data suggest a really address the core problem of overfitting. mean of about 27 minutes for all acts, and a standard A second approach to model comparison is to penalize deviation of about 3 minutes (Cutting, 2016). Polyno- model complexity (models that have more parameters). mial curves should accommodate these differences There are many ways to do this (see, for example, when averaging over the slightly different-length acts Myung, Tang, & Pitt, 2010). For example, using adjusted of different movies. R2 values is one way to handle this problem in regres- Nonetheless, using polynomials to fit data can lack the sion situations, a procedure I follow here. Unfortunately, appropriate conservativeness in statistical analysis. This this method is widely agreed to underestimate overfitting is because high-parameter count models easily lead to (Stauffer, 2008, p. 267). Moreover, across the plenum of false-positive results. The reason for this is that all mul- multivariate analyses, there is debate about how much tivariable modeling is prone to overfitting, and the more penalty should be levied. parameters in the model, the more likely it will fit “too A third solution, and one preferred in machine learning well.” Thus, model results may appear more robust than and elsewhere, is cross-validation (see, for example, they really are because they fit with equal felicity both a Browne, 2000), sometimes called within-sample prediction. theoretical pattern underlying the data and the random That is, one splits the data into two groups, runs the ana- noise buried within it (Cutting, 2000; Pitt & Myung, 2002). lysis on the first dataset (called the training set), and then One solution to overfitting is to prefer simpler models uses the model form and its parameter values in a to those that are more complex and that do not reliably parameter-free assessment of the other set (the test set). If Cutting Cognitive Research: Principles and Implications (2016) 1:30 Page 7 of 21

both fits are comparable and statistically reliable, this can Modal pacing across the sound era, 1930–2015 be called a replication. If the fit to the test data does not Again, the three dimensions investigated here are the yield a reliable result, then the first results are said to be mean shot durations measured by transition density, the due to overfitting. mean amount of flicker motion as measured by inter- In practice, it is good to do this procedure many times, frame correlations, and the mean luminance across all so, in the cross-validation analyses performed here, I frames of shots in the 180 sound movies released from randomly split the data in half 10,000 times, then take 1930 to 2015. Again, these are related to the film studies the averages across all training and all test fits.6 The notion of pace, and they are the pertinent film-style vari- mean of the adjusted R2 values across the training sets ables to consider because, through componential analysis, should approach the adjusted R2 value for the means of Cutting (2016) found them to align with three orthogonal bins in the whole dataset, and the mean of the un- stimulus dimensions encompassing perhaps all of the vari- adjusted R2 values across the test sets should be only a ous correlated dimensions of film style. Figure 1 shows bit less. Of importance in this context is whether the test three panels of mean data, each of which represents set mean R2 value is statistically reliable. Because after a 18,000 data points culled from almost 2 trillion pixels. cross-validation run the training results are parameter- less, the comparison between the training means and Study 1: dynamic patterns of shot durations across the the test data means affords a two-sample correlation test length of movies on which a t value can be calculated. If this value is suf- The left panel of Fig. 1 expands on the data from Cutting ficiently great (again, here α = .0001), I will take such a (2016, study 1; see also Cutting, Brunick, & DeLong, 2012). finding as a second confirmation that the initial polyno- It presents the mean pattern of shot durations across the mial fit is a reliable result. In this article, I will accept re- 100 duration-normalized time bins for the 180 movies. sults across the 100 bins only if the polynomial fit is The red line shows the best-fitting sixth-degree polynomial confirmed in both ways,7 although some interesting situa- (t[93] = 6.03, p < .0001, adjusted R2 = .64). This fit is reliably tions arise and are worth discussing when the polynomial superior to the best fits of all lower-order polynomials (ad- fits are not corroborated by cross-validation. justed R2 = .51, .47, .33, .26, and .25, respectively, for the Finally, I will display the data in a manner that reveals fifth-order polynomial down through the linear fit). Ten both its variability and its underlying trends. To do this, I thousand cross-validation trials on random halves of the will show four things: (1) the individual mean bin data data yielded results for sixth-order polynomials on training points will be in black; (2) the line of the best polynomial data nearly comparable to those for the whole dataset (ad- fit is shown in a given color (red for shot duration, blue to justed R2 = .56), and the test results are almost as strong motion, and green for luminance); (3) the 95% confidence (unadjusted R2 = .42, t[98] = 8.42, p < .0001, d = 1.7). Thus, interval on those polynomials will surround that line as a one can be quite confident that this polynomial is a reason- clear region; and (4) the 95% confidence interval of the able representation of the trend underlying the data. data given that polynomial can be seen in a slightly lighter In the left panel, the sequence of 100 bins is also color of red, blue, or green. When the polynomial fits are broken into 4 equal-length regions, following the sugges- reliable but the cross-validation results show that these are tion by Thompson (1999): the setup (again, roughly bins likely due to overfitting, I will show the overall trend in the 1–25), the complication (bins 26–50), the development data as a solid 95% confidence interval of the data on the (bins 51–75), and the climax (bins 76–100). The two op- linear fit, even if that linear fit is not reliable. Within that tional subsections also leave their marks on shot dur- region, I will show a candidate higher-order polynomial ation. The end of the climax often contains an epilogue that failed cross-validation as a line in a contrasting color. where a new diegetic (film-world) order is established Because the focus of this article is on the dynamic pat- and loose ends are tied up (Thompson, 1999), and the terns across the length of movies, I will try to determine beginning of the setup often contains a prologue in when they first arose in the history of popular feature- which the setting, the time period, and the protagonist length cinema. To do this, I will start with the 180 movies are introduced (Cutting, 2016). from the sound era to establish general patterns, then Notice two striking features within the four acts, both work backward through time in divisions within this sam- of which make narrative sense. First, the shot durations ple, and finally consider those of the silent era to see how of the setup are initially long in the prologue but recipro- these patterns may have developed. Studies 1–3willbegin cally shorten as the bin number increases (1/1, 1/2, 1/3, by exploring the global patterns across the whole of the etc.; t[22] = 8.64, p < .0001, d = 3.7), helping to ease the sound-era sample; studies 4–6 will address the different viewer into the narrative. The subsequent shot durations eras of sound film (1995–2015, 1960–1985, and 1930– are noisily varied but relatively steady through the com- 1955) for each of the dimensions; and studies 7 and 8 will plication and development, but then the second major consider their possible roots in silent movies (1915–1925). feature is the decline of shot duration in the climax is Cutting Cognitive Research: Principles and Implications (2016) 1:30 Page 8 of 21

followed by marked increase in the epilogue as the nar- green, and again the lower-order polynomial fits do rative returns to diegetic normality (quadratic trend, reliably less well (adjusted R2 = .64, .34, and .30). Cross- t[22] = 2.71, p =.02,d = 1.15). Cutting (2016) also reported validation results are again quite good, with sufficiently that the shot durations in the development were slightly similarresultsfortraining datasets (mean adjusted longer than those in the complication, but in this ex- R2 = .57) and test datasets (mean unadjusted R2 = .26, panded sample, this difference, although present, is not re- t[98] = 5.93, p < .0001, d =1.20). liable. Visual inspection suggests that the decline in shot There are two striking trends across this luminance durations starts earlier, before the end of the complication, profile. First, there is a strong darkening across the nullifying the possible result. complication and development (bins 26–75, t[48] = 12.66, As noted above, I have divided the movies into four p <.0001, d = 3.65), and second, this is followed by a eras – silent (1915–1925), early (1930–1955), middle strong brightening through the climax and epilogue (bins (1960–1985), and near-contemporary (1990–2015). In the 76–100, t[23] = 4.94, p <.0001,d = 2.06). Less obvious, but shot duration data across the 180 sound movies, there is a similar to the pattern in the left panel of Fig. 1, there is a reliable bin × movie era interaction (early vs. middle vs. marked tightening of the confidence interval during the contemporary, F[2, 17,994] = 10.52, p < .0001), denoting prologue. Finally, there was a reliable interaction of bin × that the dynamic pattern has changed over 85 years. This movie era (F[2, 17,994] = 5.96, p = .0026), suggesting for a result presages evolutionary trends and is sufficiently im- third time that the dynamic patterns have changed over portant to pursue in study 4. time. This effect will be pursued in study 6.

Study 2: dynamic patterns of motion across the length of Pace, attention, and emotion: preliminary conjectures movies Cuts and Shot Durations. The psychological import of The middle panel of Fig. 1, expanding on Cutting (2016, the overall pattern of the results of study 1 stems from study 3), shows the general pattern of flicker motion across the relationship between cuts and eye movements. Smith the length of the 180 sound movies. Again, a sixth-order (2012, 2013) reported that cuts are generally associated polynomial, shown in blue, is reliably superior to others with later eye movements. Viewers typically saccade (t[93] = 5.17, p < .0001, adjusted R2 = .57, with decreasing back in the direction of the center of the screen. Again, lower-order adjusted R2 = .45, .34, .34, .33, and .20, this result seems consistent with filmmakers’ goals about respectively). Ten thousand cross-validation trials pace. It suggests that movie viewers should be particu- yielded similar results for the training data (mean ad- larly attentive during the climax, driven by the content justed R2 = .47) and more than acceptable results for the of the narrative. Similarly, the increase in cut frequency test data (mean R2 =.26,t[98] = 5.83, p <.0001,d =1.18). across the prologue into the remainder of the setup Again, several striking patterns are apparent that make could serve to increase eye movements and possibly at- narrative sense. In particular, there is a linear decline in tention, bringing the viewer into the plot. Symmetrically, motion through the setup as narratives settle down and the decreasing pace and eye movement demands of the the first conversations occur (bins 1–25, t[23] = 3.95, epilogue should help bring the viewer back out. p = .0006, d = 1.64), followed by another noisy oscilla- Motion. Mital and colleagues (2011) showed that mo- tion through the complication and development. This tion attracts viewers’ eye movements, and hence atten- is then followed by a sharp rise in motion during the tion, when they watch movies. This, too, suggests that climax and a steep decline in the epilogue (quadratic engagement in the movie may be greatest during the fit, t[22] = 3.17, p = .005, d = 1.35). A bit less obvious is middle of the climax. Further, and more speculatively, the reduction of the confidence interval at the beginning motion has been shown to affect the perception of the of the prologue. The reason for this will become clearer in passage of time (Brown, 1995), dilating it (making it study 5. Finally, as with shot durations, there was an inter- seem longer) at short durations. This might give the action of bin × movie era (F[2, 17,994] = 8.16, p =.0003), viewer a sense of increased processing speed, which can giving another hint of the evolution of motion as a com- be associated with positive affect and well-being (Pronin, ponent of film style. This result is pursued in study 5. 2013). Moreover, continued fast processing speed and al- ternating thoughts – such as those engendered by the Study 3: dynamic patterns of luminance across the length cross-cut scenes of a protagonist and antagonist in the of movies climax of action films – can create anxiety (Pronin & Finally, the right panel of Fig. 1 expands on the results of Jacobs, 2008), which is exactly the goal of most action Cutting (2016, study 4), showing the patterns of change in film narratives. mean frame luminance across the length of the 180 sound Luminance. Finally, consider the nadir of the lumi- movies. The 100 bins are fit well by a fourth-order polyno- nance function. This ¾ point in movies is often called mial (t[95] = 4.18, p <.0001,adjusted R2 = .70), shown in the “darkest moment” in a movie narrative (Bordwell, Cutting Cognitive Research: Principles and Implications (2016) 1:30 Page 9 of 21

2008; Keating, 2011). It occurs at the end of the develop- Changes in pacing across the sound era, 1930–2015 ment section, when events seem to be most stacked With these expanded overall dynamic patterns in place, against the protagonist in trying to achieve her goals. As I now focus on trying to determine when they arose. Cutting (2016) noted, this “darkest moment” is not sim- Will these same higher-order polynomials be found in ply a metaphor: On average, movies typically project the patterns of all movies across the century-wide sample? their least luminous images at about this point. Similarly, The three bin × movie era interactions suggest not. the beginning of the complication, also called the ¼point, can be considered the brightest point (Lucey, 1996), or at Study 4: changes in shot duration patterns leastthepointmarkedbyaprotagonisttakingonher Movies from 1990 to 2015. As shown in the right panel particular quest. Moreover, Smith (2015) noted that the of Fig. 2, the pattern of shot durations for the 60 most protagonist’s despair at the ¾ point provides maximal contemporary movies essentially mimics that for the larger contrast with the outcome of the narrative, here at the collection of all sound movies. Again, as in study 1, it is end of the epilogue, where she typically has conquered best fit by a sixth-order polynomial (t[93] = 8.22, p < .0001, her difficulties. In luminance terms, this is literally true; adjusted R2 = .69), which is superior to all lower-order fits epilogues are often the brightest sequence of a movie. (adjusted R2 = .47, .34, .17, .17, and .16) and which cross- Thus, and again, film style has appeared to mesh with validation affirmed (mean training set adjusted R2 =.58; the pacing goals of filmmakers. How effective this manipu- mean test set unadjusted R2 = .41, t[98] = 8.25, p < .0001, lation is for the viewer is unknown, but it seems to be an d = 1.67). The two major features of the general results appropriate adjunct to the content of the narrative. in the left panel of Fig. 1 are here corroborated: The Demonstrating these three congruences – the yoking negative exponential decline in shot duration across the of the aspects of pace and film style to the progression setup is again robust (t[22] = 7.56, p <.0001, d = 3.2), and of narrative events – was exactly the intent of Cutting the quadratic trend in the climax is as well (t[22] = 6.09, (2016). Here, these results expand those to a broader p < .0001, d =2.6). corpus and time frame. Future research is needed to tie Thus, the pattern for the more recent movies matches these patterns more directly to viewers’ responses. How- quite well the average pattern of the 180 movies from ever, the main goal of this research effort is to trace 1930 to 2015. Of course, the former are contained within when these congruences arose. the latter, but, among other things, this result suggests that

Fig. 2 Variations in mean shot duration (in seconds) across the duration-normalized films of three different eras of popular movies. The extents of the vertical axes show equal variance in the data across the three panels. The statistical lines and regions of the middle and right panels are as they were in Fig. 1; there is no reliable pattern in the left panel. Vertical lines in all panels separate the bins into the four narrative sections, as in Fig. 1 Cutting Cognitive Research: Principles and Implications (2016) 1:30 Page 10 of 21

the overall pattern, if not pervasive across time, may at stylistically there is a bit more anticipation of action in least have bin regions that are not too discrepant from the complication of movies of this era than in those those shown in the left panel of Fig. 1. that are more contemporary. In other words, the pat- Movies from 1960 to 1985.Themiddle panel of Fig. 2 tern of shot durations in movies from 1960 to 1985 is shows the pattern of shot durations from the middle generally similar, but not identical, to those from 1990 chronological group of 60 sound films. This pattern is best to 2015. The overall later form is nascent but not fully fit by a fourth-order polynomial (t[95] = 4.81, p < .0001, present in the midsample movies. adjusted R2 = .51), which is superior to lower-order fits Movies from 1930 to 1955.Theleft panel of Fig. 2 (adjusted R2 = .39, .29, and .28). Cross-validation corrobo- shows a result not seen before. There is no reliable pattern rated the main result (mean training set adjusted R2 =.41; among the shot durations of the earliest sound movies. mean test set R2 = .29, t[98] = 6.32, p < .0001, d = 1.28). For display purposes, the data are graphed showing the Finally, there was a modest interaction between the 95% confidence interval on the data on a linear regression bin values of the more contemporary movies (1990– line, but even that line isn’t significant. Moreover, there 2015) and those of these midrange movies (1960–1985; was a sizable interaction of bins × movie era, early (1930– F[1, 11,996] = 5.32, p = .02). Thus, the patterns of the 1955) vs. midsample (1960–1985; F[1, 11,995] = 18.5, middle and right panels of Fig. 2 are a bit different. p < .0001). Thus, the stylistic patterns of shot durations Two features in the pattern of the middle sample seen in the left panel of Fig. 1 appear to have developed movies differ from that of the latter films. These are cap- slowly throughout the 20th century. tured in the decrease in polynomials from sixth order to fourth order. In short, the pattern is less articulated. For Study 5: changes in motion patterns example, the lengthening of shots in the epilogue is not Movies from 1990 to 2015. As seen in the right panel of nearly so marked as in the later movies, suggesting less Fig. 3, the pattern of motion across the 100 bins is best contrast between the action of the typical climax and the fit by a fifth-order polynomial (t[94] = 4.99, p < .0001, calm of the typical epilogue. In addition, the decline in adjusted R2 = .45), which is superior to lower-order shot duration is extended from the complication through polynomial fits (adjusted R2 = .30, .29, .18, and .12). to the point in the climax where the epilogue weakly Cross-validation confirmed this pattern (mean training turnstowardlonger-durationshots.Thissuggeststhat trial adjusted R2 =.35;meantesttrialR2 =.16,t[98] = 4.32,

Fig. 3 The mean flicker motion variation across the duration-normalized movies in three different eras of popular movies. The extents of the vertical axes show equal variances in the three datasets. Again, the statistical lines and regions of the middle and right panels are as they were in Fig. 1; there is no robust pattern in the left panel,butthepurple line shows a reliable polynomial pattern that fails cross-validation. Vertical lines in all panels separate the bins into four narrative sections Cutting Cognitive Research: Principles and Implications (2016) 1:30 Page 11 of 21

p <.0001,d = 0.87). Again, as in study 2, there is a decline the early (1930–1955) and midsample (1960–1985) movies in motion across the setup (t[23] = 5.62, p < .0001, d = is reliable (F[1, 11,995] = 15.36, p < .0001). Thus, as with 2.34) and a quadratic trend in the climax (t[22] = 6.12, shot durations, it is clear that the general pattern of motion p < .0001, d =2.6). in movies emerged relatively slowly and became more artic- The difference in results between the larger group of ulated across the century. sound movies and the more recent subset is again one of polynomial rank – sixth order for the 180 movies and Study 6: changes in luminance patterns fifth order for the 60 more recent ones. A comparison of Movies from 1990 to 2015.Theright panel of Fig. 4 shows the middle panel of Fig. 1 and the right panel of Fig. 3 the pattern of luminance across the length of movies shows the major difference to be in the first five or so bins, was, as in study 3, best fit by a fifth-order polynomial the general extent of the prologue, in both means and (t[95] = 5.41, p < .0001, adjusted R2 =.63), which is confidence intervals. This suggests that the newer movies superior to the lower-order fits (adjusted R2 = .52, .10, are much more likely to start with greater motion than and .03). Cross-validation yielded affirming results older ones, likely explaining the tightening of the confi- (mean training set adjusted R2 = .49; mean test set R2 = .23, dence interval in the middle panel of Fig. 1. The style of t[98] = 5.67, p < .0001, d = 1.14). Again, the decline in lumi- contemporary movies seems better geared to engross the nance across the complication and development is striking viewer earlier in the film, bringing her into the narrative. (t[48] = 8.03, p < .0001, d = 2.3), as is the linear rise through Movies from 1960 to 1985. The motion results of the the climax (t[23] = 6.61, p < .0001, d =2.75). middle-era movies are quite different, as shown in the The pattern for the more recent movies has a polyno- middle panel of Fig. 3. These data are best fit by a mial fit of the same order as the entire group of sound quadratic function (second-order polynomial, t[97] = 4.28, movies. A comparison of the right panels of Figs. 1 and p < .0001, adjusted R2 = .37), which is superior to the linear 4 shows that the reduction of the 95% confidence interval fit (adjusted R2 = .15). Cross-validation confirms this result on the polynomial fit is in the prologue for both the 180 (mean training set adjusted R2 = .24; mean test set R2 = .15, movies and the most recent 60 movies. This suggests t[98] = 4.15, p < .0001, d = 0.84). that filmmakers’ decisions about the initial luminance Here we have a drop in polynomial fit from fifth-order composition of movies remains quite fluid. Again, the to second-order, showing less articulation in the data. most prominent result is the progression across the However, the difference is subtler than it might first ap- complication and development of increasing darkness, pear; there is no reliable bin × movie era interaction matching the increasing narrative difficulty for the pro- (1960–1985 vs. 1990–2015 movies; F = 1.11, not signifi- tagonist, followed by the striking rise in luminance as cant). Nonetheless, gone in the fit to the midsample things turn out well. Again, film style corroborates nar- movie data are the systematic decreases in motion in rative form. both the prologue and the epilogue. There is no system- Movies from 1960 to 1985.Themiddle panel of Fig. 4 atic interaction across the two classes of film for the pro- shows that there is no reliable luminance pattern at all logue shown in bins 1–10, but there is a small difference over this period. For display purposes, the data are in the epilogue shown in bins 90–100 (t[1316] = 3.07, bounded within the 95% confidence interval of a nonre- p < .0022, d = 0.17). The expansion of the confidence liable linear fit for comparison with panels in the other interval in the epilogue suggests that movies differ in figures. A third-order polynomial, the purple function whether their motion retards at this point or not. The within the green background and having the same decline only residual effect is the increase in motion in the de- over the complication and development, showed some velopment and through the climax. promise as a successful model (t[96] = 4.94, p <.0001,ad- Movies from 1930 to 1955. The pattern of motion re- justed R2 = .42), but cross-validation suggested that this re- sults for the oldest sound movies is shown in the right sult was due to overfitting. The mean training set fits were panel of Fig. 3. As there was for shot durations of this reasonable (adjusted R2 = .30), but the mean test set data movie era, there is no reliable pattern here for motion. yielded no support for this function (R2 <0).Thus, and Data are again shown within the 95% confidence band of again, there is a hint of a trend in these data similar to that a linear regression, which itself is not statistically reli- found in later films. Nonetheless, the pattern of luminance able. However, a sixth-order polynomial did yield a mar- across bins is different between the more contemporary ginal result (t[93] = 3.17, p = .002, adjusted R2 = .17), movies and the midrange movies (F[1, 11,996] = 7.69, although it failed cross-validation (training set adjusted p = .006). R2 = .15, test set R2 < 0).8 The point here is that buried Movies from 1930 to 1965. Shown in the left panel of within the essentially random data is a suspicion of a Fig. 4 are the luminance data for the movies from the pattern that bears some resemblance to the middle panel earliest sound era. These show a significant linear de- of Fig. 1. Nonetheless, the interaction between bins and cline (t[93] = 6.85, p < .0001, adjusted R2 = .32), with the Cutting Cognitive Research: Principles and Implications (2016) 1:30 Page 12 of 21

Fig. 4 The mean luminance variation across the duration-normalized movies in three different eras of popular movies. The extents of the vertical axes show equal variance in the three datasets. Again, the statistical line and regions of the left panel are as they were in Fig. 1; here, there is no robust pattern in the left or middle panel, but the purple lines show statistically reliable patterns that failed cross-validation. Vertical lines in all panels separate the bins into four narrative sections cross-validation results not quite corroborating that find- live action shots to be very long or quite short in dur- ing by my criterion (training set mean adjusted R2 =.21; ation. Unsurprisingly, luminance is also affected (title test set mean R2 = .09, t[98] = 3.11, p < .003, d =0.63). slides are dark) and so is motion (ideally there is no mo- In addition, there was no reliable interaction in lumi- tion in a title slide, although a bit of jitter is quite com- nance between the early sound films (1930–1955) and mon). In addition, the distribution of the intertitles is those that came later in the 20th century (1960–1985; not uniform throughout the length of the movie. Almost F <1). every silent film begins with one or more title slides, It seems possible that the hint of a linear trend over and, amassed over 20 duration-normalized bins, they be- the whole film may be a precursor to the future linear come linearly less frequent as the movie progresses trends over just the complication and the development. (t[18] = 4.25, p = .0005, d = 2.0). Nonetheless, it also appears that the full-blown pattern Compositionally, there are two types of intertitles – of luminance shown in the right panel of Fig. 1 did not dialogue titles and expositional titles (see Salt, 1992). fully emerge until the end of the 20th century, and pos- The former occur within scenes and were rare before sibly later than the shot duration and motion patterns. about 1913; the latter typically introduce scenes and began to appear incrementally in about 1901, often with Pacing in the silent era text surrounded by artistically illustrated scroll patterns. Perhaps nascent forms of these trends in shot duration, Although dialogue intertitles are long gone from sound motion, and luminance can be found in silent movies. movies, expositional intertitles have not completely dis- To be sure, direct comparison of sound movies and si- appeared. For example, they can be found in Goodfellas lent movies in this context is difficult. The reason is that (1990) and Avengers: Age of Ultron (2015) and are often about 15% of the screen time in this sample of 30 silent present in the films of Quentin Tarantino (Cartmell, 2012). movies is taken up by intertitle shots – text printed in Intertitles also had a special status in early filmmak- white on black. These affect the distribution of shot du- ing; scriptwriters and intertitle writers were rarely the rations. Although the mean duration of intertitle shots same person, and there was even one Academy Award in this sample (7.27 seconds) is about the same as that in 1929 given for title writing (Cartmell, 2012). In for live action shots (7.41 seconds), their variability is addition, intertitles were not simply add-ons after the not (σ = 3.9 seconds for intertitles, 6.8 seconds for live- moviewasshot;theywereembeddedinthedesignof action shots). In other words, it is much more likely for the film at its conception. Cutting Cognitive Research: Principles and Implications (2016) 1:30 Page 13 of 21

But again, for my purposes, intertitles are a nuisance. used elsewhere (mean training set adjusted R2 =.28;mean They play havoc with each of the analyses that I have test set R2 =.07, t[98] = 2.71, p = .008). These results are undertaken and may disrupt the psychological effects shown in the top left panel of Fig. 5, with the blue line that film style patterns might afford. Nonetheless, in showing the fit. To be sure, the long prologue shots are hopes of finding some patterns that are useful to compare often associated with complex and often multiple interti- with the sound films, I analyzed the silent movies in two tles, and the long epilogue shots are also often similar ways – first with the intertitles considered as regular shots intertitles projecting events of the narrative future. But and second with the intertitles stripped out and the there is even a quadratic trend in the climax and epilog remaining shots abutted as if the former did not exist. (t[22] = 2.80, p =.01,d =1.19). Moreover, there isn’t even a significant interaction in Study 7: silent movies with their intertitles the shot duration patterns between the silent movies Shot Durations. Perhaps the biggest surprise of this set and the contemporary sound movies of 1990–2015 (F[1, of studies is that the sixth-order polynomial was signifi- 8997] = 2.52, p > .10). Thus, there is a sense in which it cant for the silent movies (t[93] = 5.51, p <.0001,adjusted took popular movies 60 years (from 1930 to 1990) to re- R2 = .43) and was superior to the lower-order polynomials capture the shot duration profile that silent movies seem (adjusted R2 = .28, .21, .09, .07, and .03). Indeed, it only to have had from 1915 to 1925. Nonetheless, one should narrowly missed cross-validation by the same criterion as be cautious inferring too much here. The silent era data

Fig. 5 In the 30 silent movies of this sample, there are no reliable patterns of shot duration, motion, or luminance that survive cross-validation, regardless of whether the shots of intertitles are included in the analysis. However, the pattern of shot durations and luminance with intertitles and motion without intertitles showed statistically reliable polynomial fits, but these failed cross-validation Cutting Cognitive Research: Principles and Implications (2016) 1:30 Page 14 of 21

are very noisy, sufficiently so that there was no reliable 2010). However, the typical movie of the last 70 years difference in shot duration patterns for the silent vs. the opens with a prologue. Shots are relatively long in dur- early sound movies either (F < 1). ation; they are wide shots (people fill relatively little of the Motion and Luminance. As shown in the upper middle screen); they are occasionally coupled with dissolves rather panel of Fig. 5, there were no systematic patterns for than cuts; they may jump across time and place; they are motion. There was, however, a slight difference be- covered with nondiegetic (background) music; they typic- tween motion patterns in the silent vs early sound ally show few conversations; and they are often covered movies (F[1, 8996] = 7.98, p = .005). This is perhaps not with title credits (Cutting, 2016). The latter might seem to surprising, because in this analysis the silent movies in- account for much of this structure, but all of these features clude intertitles. except being covered with title credits (which began in this The luminance pattern in the silent era revealed a suspi- sample in 1960) existed in the early live action shots of cion of a third-order polynomial fit in the luminance data movies in the two decades before, when opening credits (t[96] = 5.79, p < .0001, adjusted R2 = .33), but although in were title cards (printed lettering, typically in black on cross-validation the training data mean is reasonable (ad- white). justed R2 = .15), the test data mean is not (R2 < 0). More- In the silent era, and even into the 1930s and 1940s (A over, there was a considerable difference in the luminance Tale of Two Cities, 1935; Mutiny on the Bounty, 1935; pattern for silent vs early sound movies (F[1, 8996] = 25.7, Foreign Correspondent, 1940), introductory narrative in- p < .0001), but again the silent movie data include their formation about time and place was typically carried by intertitles. one or more expository intertitles. Thus, long-duration live action shots were not used. After these intertitles, Study 8: silent movies stripped of intertitles shots also had little motion; however, over the last The lower panels of Fig. 5 show that there is no evidence 60 years, the prologue has gradually become one of the of any trend across the length of silent movies in their most active sections of movies, but still with shots rela- shot durations, motion, or luminance profiles when inter- tively long in duration. These often include pans and titles are removed. In addition, there were also no reliable tracking shots of the initial settings of the narrative. differences between the shot duration, motion, and lumi- The purpose of the structure of prologue shots appears nance patterns across silent movies with and without their to be to bring the viewer down into the narrative. Often intertitles (all F[1, 5996] < 2.2, all p >.10). Somewhat this is literally true; in The Hunt for Red October (1990), surprisingly, there was a modest fourth-order polynomial for example, we first hover over a digital globe that ro- fit to the motion data (t[95] = 2.33, p = .025, adjusted tates, first showing the United States and then Russia, R2 = .16), but this did not survive cross-validation in and then in live action we look down on snowcapped either the training trials (adjusted R2 = .15) or the test mountains near Murmansk. In MASH (1970), we first trials (adjusted R2 <0). look down on a helicopter flying over the mountains of One might claim that the lack of patterns in the data Korea (the stand-in for Vietnam) before then looking up for silent movies with and without their intertitles is as it lands. In East of Eden (1955), we look down on the caused by mixing movies with different act structure – Monterey, California, coastline. Such shots create an at- some with three equal-length acts and some with four. mosphere and inform the viewer about the locations and Although this is entirely possible, the beginnings of the time periods of the narrative. Background music also setups and the ends of the climaxes should align in both helps create calm, or anxiety, or whatever emotion is ap- cases, and yet there is no evidence in the data shown in propriate to the situation (Kalinak, 2010). Fig. 5 that would affirm this possibility. There then follows an almost seamless glide into the setup and the narrative proper. Shot durations shorten General discussion but not too rapidly, and motion diminishes, but in con- Conjectures on how pace has converged on narrative temporary movies again not too fast. Background music, form which set the emotional tone for the beginning of the As a recap, let me proceed through the sequential narra- film, typically drops out, and conversations begin, often tive structure of movies and outline the changes in film with the protagonist involved – at least 80% of all pro- style, when they occurred. I will also suggest possible logues introduce the protagonist (Cutting, 2016). The psychological reasons for them and give examples from exogenous demands for eye movements will increase as particular movies from this sample along the way. the shot-reverse shot technique (alternately showing the The prologue and the setup. Some more recent movies characters conversing) takes over. The modal pace of the have a “cold open” where the movie launches directly movie becomes established – the average shot duration into what appears to be the middle of the narrative (Die during a conversation is typically about the average shot Hard 2, 1990; Erin Brockovich,2000;The Social Network, duration of the movies – as we learn about the goals of Cutting Cognitive Research: Principles and Implications (2016) 1:30 Page 15 of 21

the characters and their circumstances. Near the end of reconciliation of a couple (Philadelphia Story, 1940); in the setup, an inciting incident often derails these goals, adventure films, it is working through some territorial dif- and a new plan of action needs to be formulated. ficulties (Back to the Future, 1985); and in mysteries, it can Complication and Development. Neither shot duration be the discovery of the solution to a crime (Psycho, 1960). nor motion has any distinctive patterns in the complica- Shorter shot durations can increase the exogenous control tion and development sections. To be sure, individual of eye position and eye movements; more motion attracts movies will vary, but the normative pattern is for relative attention; and it seems likely that the cross-cutting of consistency across these sections, where 60% of the short scenes of the protagonist and antagonist in action shots continue to show conversations, slightly more for films creates anxiety. But the increase in luminance across dramas, less for action movies. Nonetheless, changes the climax is a signal that things should turn out well. have taken place in film style that affect these narrative Of course, such a heightened state is difficult to main- sections. Mean shot duration rises from the silent era tain, and few movies try. The function of the epilogue is (about 7 seconds) to the early sound era (11 seconds), to bring the story back to diegetic normality, to tie up and then shortens markedly through the midsample loose ends, and then lift the viewer (often literally with a movies (7 seconds) to the more contemporary films rising crane shot, as in Ordinary People, 1980; Mission: (4 seconds). The decreases in shot duration in this range Impossible II, 2000; and Valentine’sDay, 2010) out of the affect exogenous eye movements and are likely to in- narrative. Longer duration shots and decreased motion crease attentional demands on the viewer. The mean place fewer exogenous demands on eye movements and amount of motion also increases steadily from the silent attention, and the continued brightening of the image era to the present, and this, too, is likely to affect eye declares that things will remain well. movements and attention, particularly in our current era of intensified continuity (Bordwell, 2006). Narrative transportation, pace, and the physical The major signal of dynamic change in the complication responses of viewers and development is in lighting, measured as overall frame Stories are the bedrock of culture. Whether by listening, luminance. Each of the four movie eras investigated here reading, or viewing, we gather critically important in- show some evidence of a decline in luminance across formation from stories. The phenomenon of our en- these sections. The evidence was weak in the silent gagement with stories is called narrative transportation movies, weak and nondiscriminating for the early sound (Gerrig, 1993; see also Van Laer, De Ruyter, Visconti, & movies (the decline covers the setup and climax as well), Wetzels, 2014). This is exactly what Griffith (1926, p. 28) and nascent for the midsample films, but it finally crystal- had in mind when he suggested that movies “lift [viewers] lized in the more contemporary films. The rationale for out of commonplace existence, and bear them … to this darkening of cinematic images appears to be con- realms of adventure and romance.” nected to the travails of the protagonist as she is thwarted Busselle and Bilandzic (2009) parsed narrative engage- in her plans to achieve her goal. Indeed, the term used for ment into four features. The first is narrative under- the end of the development is the darkest moment standing, without which there can be no thorough (Bordwell, 2006; Keating, 2011; Smith, 2015). Interestingly, engagement. Another is narrative presence (the feeling until recently (Cutting, 2016), there was no evidence that of having entered the story, typically at the cost of pay- this was literally true. This is a case where metaphor meets ing attention to our real-life surrounds). In this context, preexisting reality. I’ll take narrative understanding as granted and acknow- Climax and Epilogue. The most striking evolutionary ledge that narrative presence may be the most interesting patterns in movies have occurred in the climax and component of the four. epilogue. Silent movies showed some suspicion of de- Presence, of course, has been a key term in the domain creased shot durations and increased movement in the cli- of virtual reality since its beginning (see, for example, max, followed by their reversal in the epilogue, but the Barfield, Sheridan, Zeltzer, & Slater, 1995), capturing the early sound movies showed no trace of either. The pattern idea that the viewer is mentally present in, and has been reappeared, somewhat malformed, in the midsample transported to, a different environment. Thus, it should films and became very strong in the more contemporary surprise no one that when watching movies one can have movies. changes in heart rate (Barraza, Alexander, Beavin, Terris, Why might this pattern occur? The function of the cli- & Zak, 2015), changes in blood pressure (Miller et al., max is to bring the protagonist to a situation where she 2006), changes in electrodermal activity (Tsai, Levenson, can directly achieve her goal. In action films, this is done & Carstensen, 2000), changes in respiratory cycling (Child by physical conflict (Spectre, 2015); in courtroom dramas, et al., 2014; Tsai et al., 2000), and, when appropriate, even it is typically the lead-up to a jury’sorjudge’s decision have oxytocin (Barraza & Zak, 2009) and endorphin re- (Inherit the Wind, 1960); in romantic comedies, it is the lease (Dunbar et al., 2016). After all, watching movies is Cutting Cognitive Research: Principles and Implications (2016) 1:30 Page 16 of 21

quite a bit like watching the life around us, but with, as syuzhet’s morphology slowly into a species/niche-like Alfred Hitchcock put it, the “dull bits cut out” (Truffaut, correspondence. 1983, p. 103). Likely much of this physiological responding Make no mistake, there may be many more such cor- is caused by the content of the narrative, but quite likely it respondences beyond the three examples investigated is augmented in the manipulation by filmmakers of the here, and there also may be many dimensions of change variables investigated here – patterns of shot duration, in movies for which an evolutionary perspective is un- motion, and luminance. helpful. Nonetheless, here – in the domain of whole-film Two of the features of narrative transportation out- pace reflected in patterns of shot durations, motion, and lined by Busselle and Bilandzic (2009) fit snugly with this luminance – an evolutionary view seems unexceptionable. view – attentional focus (lack of mind-wandering) and emotional engagement (our feeling for the characters). The changes in cut frequency and motion likely contrib- Why did these changes in pace take so long? ute to the former and luminance to the latter. Do these Whether one regards these results as a consequence of patterns alone affect heart rate and the other physiological evolution or merely of a set of changes, one should ask: measures? Empirically, this would be challenging to deter- Why did it take 60 years and more – from 1915 or 1930 mine, but with enough different movies appropriately until 1990 and beyond – for the patterns shown in the measured and enough subjects, it should be possible to right panels of Figs. 2, 3, and 4 to appear? In retrospect, answer this query. these dynamic configurations of film style seem fairly obvious. Shouldn’t filmmakers have figured this out long Film style: evolution or change? ago? Continuing on the evolutionary theme, I note that Are these changes in patterns of shot duration, motion, cultural evolution, although sometimes quite rapid, need and luminance across the sound era an example of an not be (Perrault, 2012). Three factors may have masked evolution or simply of change? Moreover, might the these changes from being obvious. changes be simply an example of fashion, reflecting dif- First, when editors work on movies, almost all of their ferent time periods of moviemaking? Carbon (2010) efforts are on shots and scenes, not acts. Among other noted that fashion typically follows cyclic patterns. To be things, the editor’s task is to make shots carry the sure, there is evidence of fashion in cinema. For example, intended emotion, to meet the requirements of content, the creation of dramatic long takes in some contemporary and to make scenes have appropriate shot durations and movies, particularly through the digital knitting together motion in order for pace to sensibly build up and step of separate shots, may recall a type of cinema more com- back (Griffith, 1926; Murch, 2001; Pearlman, 2009). Each mon to the mid-20th century. A case in point is the 6- movie has many scenes, and, if one counts cross-cut minute-long opening “Day of the Dead” shot in Spectre scenes separately, over the last 7 decades, there have (2015). Long takes aside, however, there is no evidence in been between 40 and several hundred separate scenes the data presented here for a cyclic oscillation across time and subscenes of different durations in any given movie in measures of shot duration, motion, and luminance. (Cutting et al., 2012). Editors mostly work locally, and With respect to the biology, it is obvious that movies the patterns discussed here are global to the whole film. are not living entities that reproduce. Nonetheless, there I suspect that in a century of filmmaking practice, the is quite a lot of random variation in the movies of all local changes propagated locally, iteratively affecting eras along the dimensions investigated here. Griffith’s nearby scenes, passing on their local constraints until a (1926) claims aside, I found no evidence in silent films stable global pattern emerged. Such a process has been (1915–1925) and early sound films (1930–1955) of any suggested in many domains of science, from vision systematic correspondence between the structure of the (Saarinen, Levi, & Shen, 1997) to ecology (Pagnutti, fabula and the pace of the syuzhet.9 Yet, in the more Azzouz, & Anand, 2007). contemporary movies (1990–2015), those correspon- Second, filmmaking is a craft. As a craft, its required dences are strong. skills are not easily penetrated in a conscious manner. A stable narrative structure can be construed as a po- The acquisition of skill is partly a trial-and-error process tential niche. In the process of natural selection, a niche of exploring and developing technique, and the rules serves as a “habitat” for the evolution of a species’ mor- that govern the execution of the work are often more phological (and other) adaptations. If the “species” is the tacit than explicit (Polanyi, 1966). Collectively, editing syuzhet and the “habitat” is the general, four-part narrative also depends on cultural transmission, here across gen- structure of the fabula, I would claim that the “natural erations of the relatively closed society of filmmakers selection” across a century of filmmaking (the “ran- (Cutting & Candan, 2013, 2015). Or, more colorfully, as dom” explorations of filmmakers and their assessments Walter Murch noted, “You pick up the good things that of successes and failures) has brought films and their other editors are doing and you metabolize those Cutting Cognitive Research: Principles and Implications (2016) 1:30 Page 17 of 21

approaches into what you are doing, and vice versa” these results to be parts of a stable pattern if most films (Ondaatje, 2002, p. 62). parsed themselves into episodic halves like Psycho. Third, technology has almost certainly played a pivotal role. Cameras have gotten lighter and smaller, enhancing Conclusions the use of close-ups and of motion (Bordwell, 2006). One response to the general results reported here is the Film and now digital sensitivity have increased to make oft-heard refrain that Hollywood movies are formulaic.10 the bulky lighting equipment needed in earlier times less Indeed they are, but this flippant critique ignores the necessary; thus, shooting is more portable, quicker, and fact that stories in all other narrative media – novels, allows a wider range of locations. But perhaps most im- plays, opera, comics, folktales – also generally follow portant are the effects of nonlinear (nondestructive) very similar part-based formulae. Such formulae serve digital editing. This process, which began to be available many functions, from aiding memory, to holding our at- in the late 1980s and early 1990s, can be much faster tention, and offering the comfort of a familiar form than the old cut-and-paste method for analog film, and (Boyd, 2009; Miller, 1990). Indeed, the familiarity and it more easily allows for “errors” and changes. One can similarity of narrative forms help to bind a culture, to create and then see the results of one’s pacemaking in educate, and to entertain. scenes and larger film units more readily and quickly. Three aspects of film style and pace that pervade the entire length of popular movies – shot duration, motion, and luminance – have developed slowly and coherently Other cinemas, other paces over the course of the 20th century and beyond. These Finally, the purpose of this article has been to mark evo- now seem to better match the pacemaking intentions of lutionary changes in the development of movie-length filmmakers, providing information in the image that, differences in film style as manifest over a century of one may speculate, also trigger increases in eye move- popular English-language movies. Two further questions ments and other physical responses that are appropri- arise. The first is, would these results generalize to the ately allied with the story line. Thus, these newer and national films in other languages? The answer is unclear. more stable patterns should facilitate an increase in the It is not even entirely clear that four-part fabulas would engagement of the moviegoers. prevail in other cinemas. Thus, the analysis of a suffi- To be sure, it would be inappropriate to say that these ciently large sample of films from Europe, Asia, or else- changes in film style make contemporary popular movies where would provide interesting and possibly different better than older ones. Good films should be judged more results. On the other hand, the century-long dominance by the nature of their narratives than by the engagement of Hollywood movies in the global market suggests that of their viewers. The residues of engagement are likely there may be similar structures and effects worldwide, gone shortly after the viewer has left the movie theater or and thus, in pursuing any narrative-film style (fabula- turned off her DVD player, high-definition television, tab- syuzhet) link, it seems reasonable to have begun with let, or smartphone. Surely, filmmakers hope that the im- English-language films. pact of the narrative haunts the viewer’s mental life longer A second question is related: Are there other stable than that. Nevertheless, I would claim that enhancing patterns of pacing that would be plausible and effective? viewer engagement through manipulations of film style In other words, could the evolutionary product have that are congruent with the goals of the story makers and been different? It should be nearly tautological to say can serve to augment the force of the narrative; they can that a well-edited movie is well-paced, but it seems enhance the tendency for viewers to get lost in the story. probable that the form of that film’s syuzhet might sys- tematically diverge from the general patterns found here Endnotes if narratives were also quite different. Psycho (1960), for 1The word movie in this quotation from Münsterberg example, can be divided in half as if it were two movies (1916), as well as in a subsequent quote by Griffith with mostly different characters (Smith, 2009). The (1926, p. 28), substitutes for photoplay, the common shower scene seems a natural (and very early) climax, term for a feature-length movie at the beginning of the and the cleanup following that scene has something like 20th century. Photoplay was also the name of a popular the calmness of an epilogue. Both halves of the movie American magazine that covered movies and their stars have similar shot duration profiles, and each is similar to from 1911 to 1980. those of the left panel of Fig. 1 for whole movies. In 2A serious problem considering older movies is their addition, the second half (but not the first) has a motion survival. Nitrocellulose, a highly flammable material, was pattern like that of the middle panel of Fig. 1, and the the film base for movies not only in the silent era but first half (but not the second) has a luminance pattern through until 1952. Pierce (2013) estimated that only like that of the right panel. Thus, it might be possible for about 14% of silent feature films from 1912 to 1929 survive Cutting Cognitive Research: Principles and Implications (2016) 1:30 Page 18 of 21

in their originally released form, and only 11% more come Smith, and an anonymous reviewer for their comments. Aspects of this research from foreign or other release sources. Survival of films be- were presented at the Pacific Division Meeting of the American Society of Aesthetics (April 2016) in Asilomar, Pacific Grove, CA, USA, and at the Psychonomic tween 1930 and 1952 is better, but still many are lost. Society Meeting (November 2016) in Boston, MA, USA. 3Five-reel movies became more or less standard in 1915, and, at 24 frames/second, a 1000-foot reel of film Received: 2 September 2016 Accepted: 8 November 2016 would last a little over 11 minutes (see Salt, 1992). 4Total film duration was calculated from the beginning of the first live action shot until the appearance of text References material at the end of movie, often “The End.” In this Barfield, W., Sheridan, T., Zeltzer, D., & Slater, M. (1995). Presence and performance within virtual environments. In W. Barfield & T. Furness (Eds.), Virtual sample, opening credits were shown as title cards environments and advanced interface design (pp. 473–513). New York: Oxford through 1955, and these were excluded from the meas- University Press. ure. Generally, afterward opening credits were superim- Barraza, J. A., Alexander, V., Beavin, L. E., Terris, E. T., & Zak, P. J. (2015). The heart of the story: Peripheral physiology during narrative exposure predicts posed on live action shots, and these shots were charitable giving. Biological Psychology, 105(1), 138–143. doi:10.1016/j. included. biopsycho.2015.01.008. 5Adjacent frames were not correlated, because the Barraza, J. A., & Zak, P. J. (2009). Empathy towards strangers triggers oxytocin release and subsequent generosity. Annals of the New York Academy of publicly available DVDs for these movies often employed Sciences, 1167, 182–189. doi:10.1111/j.1749-6632.2009.04504.x. a digitization process that blended successive frame pairs. Barsam, R., & Monahan, D. (2013). Looking at movies (4th ed.). New York: W. W. Sometimes this mis-sampling was endemic throughout a Norton. Berndt, J. (2013). Ghostly: “Asian graphic narratives”, Nonnonba, and manga. In D. movie; sometimes it was only occasional. Stein & J.-N. Thon (Eds.), From comic strips to graphic novels: Contributions to 6A standard procedure in machine learning is to have the theory and history of graphic narrative (pp. 363–384). Berlin: De Gruyter. the training set occupy 80% of the data and the test set Bordwell, D. (1985). Narration in the fiction film. Madison: University of Wisconsin Press. occupy 20%. Such partitioning yields results a little dif- Bordwell, D. (2006). The way Hollywood tells it. Berkeley: University of California Press. ferent from splitting the sample in half, as I have done Bordwell, D. (2008). The poetics of cinema. New York: Routledge. here. Unsurprisingly, the adjusted R2 for the training set Bordwell, D., Staiger, J., & Thompson, K. (1985). The classical Hollywood cinema: Film style and mode of production to 1960. New York: Columbia University Press. becomes larger as it more closely approximates the Bordwell, D., & Thompson, K. (1997). Film art: An introduction. New York: McGraw-Hill. 2 whole set, and equally unsurprisingly, the R for the test Borst, A., & Euler, T. (2011). Seeing things in motion: Models, circuits, and set becomes smaller, given that it is less closely approxi- mechanisms. Neuron, 71(6), 974–994. doi:10.1016/j.neuron.2011.08.031. Boyd, B. (2009). On the origin of stories. Cambridge, MA: Belknap/Harvard mates the whole set. University Press. 7 When assessing portions of the 100-bin data, such as Braudel, F. (2009). History and the social sciences: The longue durée. I. Wallerstein those bins corresponding to a given act, I use the more (Trans.). Review (Fernand Braudel Center), 32(2), 171–203. Retrieved from α http://www.jstor.org/stable/40647704. conventional criterion, = .05. British Film Institute. (2012). Statistical yearbook, 2012. Retrieved from http://www. 8 2 At first blush, negative R values would seem impos- slideshare.net/carlpercival/statistical-year-book-2012. sible, but their proper interpretation is that the particular Brown, S. W. (1995). Time, change, and motion: The effects of stimulus movement on temporal perception. Perception & Psychophysics, 57(1), 105–116. doi:10.3758/ fit is worse than a linear fit. BF03211853. 9 From the 1930s, pausing through the 1950s, but ac- Browne, M. (2000). Cross-validation methods. Journal of Mathematical Psychology, celerating again thereafter, the number of shots per film 44(1), 108–132. doi: 10.1006jmps.1999.1279. has burgeoned threefold. This would mean that, given Busselle, R., & Bilandzic, H. (2009). Measuring narrative engagement. Media Psychology, 12, 321–347. doi:10.1080/15213260903287259. 100 equal-duration bins normalized to the length of Carbon, C. C. (2010). The cycle of preference: long-term dynamics of design films, there would be more noise in the number of shot properties. Acta Psychologica, 134(2), 233– 244. doi:10.1016/actpsy.2010.020.004. durations per bin. However, given 60 movies in each era Cartmell, D. (Ed.). (2012). A companion to literature, film, and adaptation. Chichester, UK: Wiley-Blackwell. of movies used here, it seems unlikely that this could Chatman, S. (1980). Story and discourse: Narrative structure in fiction and film. contribute to the difference in patterns. Ithaca, NY: Cornell University Press. … 10As of 1 September 2016, the phrase Hollywood Child, N., Hanson, B., Bishop, M., Rinaldi, C. A., Bostock, J., Western, D., Taggart, P. (2014). Effect of mental challenge induced by movie clips on action potential in movies are formulaic had gotten 3550 hits on Google. normal human subjects independent of heart rate. Circulation: Arrhythmia and Electrophysiology, 7, 518–523. doi:10.1161/CIRCEP.113.000909. Competing interests Christiansen, T. (1997). Reel politics: American political movies from Birth of a The author declares that he has no competing interests. Nation to Platoon. New York: Blackwell. Cohn, N. (2013). Visual narrative structure. Cognitive Science, 34(3), 413–452. Author Note doi:10.1111/cogs.12016. Requests for information, data, or copies of this article can be sent by postal Cohn, N. (2014). You’re a good structure, Charlie Brown: The distribution of mail to J. Cutting, Department of Psychology, Uris Hall, 109 Tower Road, Cornell narrative categories in comic strips. Cognitive Science, 38(7), 1317–1359. University, Ithaca, NY 14853-7601 USA, or by email to [email protected]. doi:10.111/cogs/12116. I thank Brandon Berman, Grant Brighter, Elizabeth Brooks, Kate Brunick, Ayse Cutting, J. E. (2000). Accuracy, scope, and flexibility of models. Journal of Candan, Jordan DeLong, Jacob Friedman, Andres Gvirtz, Catalina Iricinschi, Alice Mathematical Psychology, 44(1), 3–19. doi:10.1006/jmps.1999.1274. Lee, Elizabeth Lewis, Michael Masucci, Elise Ozbardakci, Christine Nothelfer, Cutting, J. E. (2014a). Event segmentation and seven types of narrative Isabella Poulos, Alexandria Smith, and Leigh Whitman for their help in coding discontinuity in popular movies. Acta Psychologica, 149(6), 69–77. doi:10.1016/ the shots and scenes of movies. I also thank Neil Cohn, Katrin Heimann, Tim j.actpsy.2014.03.003. Cutting Cognitive Research: Principles and Implications (2016) 1:30 Page 19 of 21

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